Lie Group Actions And The Slice Theorem

The slice theorem has been a successful tool in the study of the action of a Lie group on a manifold.This paper reviews the slice theorem for the case when the group G and the manifold M are finite-dimensional as well as Ebin’s[1]theorem for the action of the diffeomorphism group on the space of Riemannian metrics of a closed manifold.Some applications are also presented[2].